Sum of primitive roots of unity

Number theory
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Tolaso J Kos
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Sum of primitive roots of unity

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Post by Tolaso J Kos »

Let $\zeta_n$ be a primitive root of unity. Evaluate the sum:

$$\mathcal{S}= \sum_{\begin{subarray}{c} 1 \leq k \leq n \\
\gcd(k,n)=1\end{subarray}} \zeta^k_n$$
Imagination is much more important than knowledge.
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